Hamotzi/Bread exempts meal foods. So the question is- is it a meal food? Some exceptions that Shalom mentioned: Many mezonoses are safek hamotzi which you already made (ask your posek). Liquids- the minhag is not to even if it should get a bracha. Some will not make a bracha directly on ice cream since it will melt into a liquid. I argued with a local posek that there's no loss since meikar hadin liquids should get brachos, too, but he wouldn't budge since the minhag is not to make a bracha on a liquid.
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YDKAug 27 '10 at 2:39

There's a Rabbi Frand tape all about the frozen-liquid controversy; I don't know what he concludes, but I picked "yes bracha" for the quick answer above.
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ShalomAug 27 '10 at 12:12

According to Sephardi poskim all deserts require their own blessing. In most sephardi homes on shabat they typically strive to bring out something for each of the berakhot(mezunot, eitz, adamah, hakol).

Regarding mezonos (mentioned quickly in a comment on a different answer):

Bread is Hamotzi, and therefore one doesn't make a beracha on it since it is included in the Hamotzi at the beginning of the meal. Cake is Mezonos and one would make a beracha on it when it is eaten as dessert.

The question of making a beracha on a mezonos dessert depends on what is considered "Pas/Bread" vs. "Pas Haba BeKisnin/Cake". There are 3 possibilities cited in SH"A (really simplifying here):

Sweetened dough

Filled dough

Hard dough

If the desert you're eating satisfies all three, it is definitely a Mezonos (and not a Hamotzi) and therefore one makes a Mezonos when eaten as dessert. A good example are hamentaschen.

However, if it satisfies only one (possibly even two) of the conditions, no beracha.